PPT-Section 9.4 Infinite Series: “Convergence Tests”

All graphics are attributed to Calculus10E by Howard Anton Irl Bivens and Stephen Davis Copyright 2009 by John Wiley amp Sons Inc All rights reserved Introduction In the last section we showed how to find the sum of a series by finding a closed form for the nth partial sum and taking its limit. How . has an American company, like . McDonald's, . dealt with . these differing cultures? . Cultural Convergence . – increasing similarities between cultures, which is not limited to beliefs, consumer brands, and media.. Section 8.3b. Sometimes we cannot evaluate an improper. i. ntegral directly .  In these cases, we first try to. d. etermine whether it converges or diverges.. Diverges???... End of story, we’re done.. Section 9.4b. Recall the Direct Comparison Test from last class…. To apply this test, the terms of the unknown series must be. nonnegative. . This doesn’t limit the usefulness of this test,. because we can apply it to the absolute value of the series.. LO: to understand further issues about Language and Occupation. Starter: Look . at the examples below. In each case, try to explain what kind of language interaction is taking place and what form of utterance the speaker is . Convergence & Divergence Theorems. Convergence & Divergence Theorems. Convergence & Divergence Theorems. Convergence & Divergence Theorems. LO: to understand further issues about Language and Occupation. Starter: Look . at the examples below. In each case, try to explain what kind of language interaction is taking place and what form of utterance the speaker is . Series. Find sums of infinite geometric series.. Use mathematical induction to prove statements.. Objectives. infinite geometric series. converge. limit. diverge. mathematical induction. Vocabulary. In Lesson 12-4, you found partial sums of geometric series. You can also find the sums of some infinite geometric series. An . Section 8.8 AP Calculus. Def Power Series. If x is a variable, then an infinite series of the form. is called a . power series. . . Generally,. is called a . power series centered at c. , where c is a constant.. Occasionally, a series may have both positive and negative terms and not be an alternating series. For instance, the series. has both positive and negative terms, yet it is not an alternating series. One way to obtain some information about the convergence of this series is to investigate the convergence of the series. Section 10.1. Sequences. Section 10.2. Infinite Series. Section 10.3. The Integral Test. 10.4. Comparison Tests. Section 10.5. Absolute Convergence; The . Ratio and Root Tests. Section 10.6. Alternating . Consider the following sequence . , . , . , . ,…. Each term of this sequence is of the form .  . What happens to these terms as n gets very large? . In general, the . , for all positive r .  . Many sequences have limiting factors. 1 John D. Norton. Department of History and. Philosophy of Science. University of Pittsburgh. SWC Scientific World Conceptions. University of Vienna. Summer School. July 2 to July 13, 2018 . What is it?. David J. Stucki. Alerts. FYS announcement.... Pythagorean Triples & Euclid's Primes due today. Archimedes . calculations.... This worksheet will be due next Wednesday!. 12 of 40 . FYE . reports (7 days left).